Sharpen the ends of Freestlye lines
I've managed to come up with a decent result using the 2D Length and Angle settings.

I first used an Along Stroke modifier (thanks Robin Betts) for the line thickness in the Render Layer Properties -> Freestyle Line Style:


This by itself didn't do much, so messing with some other settings, I managed to get the Min 2D Angle and the 2D Length values to get me a close enough result to the one I 'm aiming for:



This may not be the best way, but for me, it works fairly well.
This is what I now have:



This way does give you different stroke widths on the mesh, giving it a more hand-drawn look which I was hoping to achieve in the first place.

EDIT: I reposted the first pic, which was originally: 



This gave the mesh occasional bumps in the lines drawn, but in case anyone wants the curves for the rendered picture above, this is what it used.